Examples are a great way to learn a new framework.
A good starting point is to download the latest source from CodePlex.
When your app starts-up, Calcium needs its IoC container created and a few default services registered.
You can do this by calling Outcoder.ApplicationModel.CalciumSystem.Initialize() method, as shown:
var calciumSystem = new CalciumSystem();
CalciumSystem.Initialize() takes the guess work out of configuring Calcium.
Call it during your app's start-up sequence.
For UWP, Windows Phone, or WinRT apps it should be called upon Launch or Activation,
and for WPF it can be within your app's constructor.
For an example of how to configure Calcium when your app launches,
see the UWP app at Trunk/Source/Calcium/Uwp/Installation/Calcium.Installation.Uwp.sln within the source repository.
In particular, you'll notice that the Bootstrapper class performs Calcium's initialization.
In-depth articles are available for specific platforms.